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An Inertial Forward–Backward Splitting Method for Solving Modified Variational Inclusion Problems and Its Application

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  • Kamonrat Sombut

    (Department of Mathematics and Computer Science, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi (RMUTT), Pathum Thani 12110, Thailand
    Applied Mathematics for Science and Engineering Research Unit (AMSERU), Department of Mathematics and Computer Science, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi (RMUTT), 39 Rungsit-Nakorn Nayok Rd., Klong 6, Khlong Luang, Thanyaburi, Pathum Thani 12110, Thailand)

  • Kanokwan Sitthithakerngkiet

    (Applied Mathematics for Science and Engineering Research Unit (AMSERU), Department of Mathematics and Computer Science, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi (RMUTT), 39 Rungsit-Nakorn Nayok Rd., Klong 6, Khlong Luang, Thanyaburi, Pathum Thani 12110, Thailand
    Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok (KMUTNB), Wongsawang, Bangsue, Bangkok 10800, Thailand)

  • Areerat Arunchai

    (Department of Mathematics and Statistics, Faculty of Science and Technology Nakhon Sawan, Rajabhat University, Nakhon Sawan 60000, Thailand)

  • Thidaporn Seangwattana

    (Applied Mathematics for Science and Engineering Research Unit (AMSERU), Department of Mathematics and Computer Science, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi (RMUTT), 39 Rungsit-Nakorn Nayok Rd., Klong 6, Khlong Luang, Thanyaburi, Pathum Thani 12110, Thailand
    Faculty of Science Energy and Environment, King Mongkut’s University of Technology North Bangkok, Rayong Campus (KMUTNB), Rayong 21120, Thailand)

Abstract

In this paper, we propose an inertial forward–backward splitting method for solving the modified variational inclusion problem. The concept of the proposed method is based on Cholamjiak’s method. and Khuangsatung and Kangtunyakarn’s method. Cholamjiak’s inertial technique is utilized in the proposed method for increased acceleration. Moreover, we demonstrate that the proposed method strongly converges under appropriate conditions and apply the proposed method to solve the image restoration problem where the images have been subjected to various obscuring processes. In our example, we use the proposed method and Khuangsatung and Kangtunyakarn’s method to restore two medical images. To compare image quality, we also evaluate the signal-to-noise ratio (SNR) of the proposed method to that of Khuangsatung and Kangtunyakarn’s method.

Suggested Citation

  • Kamonrat Sombut & Kanokwan Sitthithakerngkiet & Areerat Arunchai & Thidaporn Seangwattana, 2023. "An Inertial Forward–Backward Splitting Method for Solving Modified Variational Inclusion Problems and Its Application," Mathematics, MDPI, vol. 11(9), pages 1-16, April.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:9:p:2107-:d:1135999
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    References listed on IDEAS

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    1. Jamilu Abubakar & Poom Kumam & Abdulkarim Hassan Ibrahim & Anantachai Padcharoen, 2020. "Relaxed Inertial Tseng’s Type Method for Solving the Inclusion Problem with Application to Image Restoration," Mathematics, MDPI, vol. 8(5), pages 1-19, May.
    2. Songnian He & Caiping Yang, 2013. "Solving the Variational Inequality Problem Defined on Intersection of Finite Level Sets," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, May.
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